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THE  AMERICAN  SOCIETY  OF 
MECHANICAL  ENGINEERS 

29  WEST  THIRTY-NINTH  STREET,  NEW  YORK 


THE  MEASUREMENT  OF  VISCOSITY 

AND 

A NEW  FORM  OF  VISCOSIMETER 

BY 

H,  C.  HAYES 

AND 

G.  W.  LEWIS 


To  be  presented  at  the  Spring  Meeting  of  The  American  Society 
of  Mechanical  Engineers,  New  Orleans,  La.,  April  11  to  14,  1916. 


THE  MEASUREMENT  OF  VISCOSITY 

AND 

A NEW  FORM  OF  VISCOSIMETER 

By  H.  C.  Hayes  and  G.  W.  Lewis 
ABSTRACT  OF  PAPER 

This  paper  deals  with  the  measurement  of  viscosity.  It  predicts  the  errors 
which  are  introduced  by  the  various  types  of  viscosimeters  and  verifies  these  pre- 
dictions in  case  of  the  short  capillary  types  such  as  the  Saybolt,  Engler,  and 
Redwood  and  the  orifice  types  such  as  the  Carpenter,  by  comparing  the  temper- 
ature vs.  viscosity  curve  for  a light  and  a medium  lubricating  oil,  as  given  by. 
these  meters,  with  the  true  curves  as  determined  by  a modified  form  of  Poiseuille’s 
capillary  tube  method. 

The  work  shows  that  the  short  capillary  types  give  results  about  50  per  cent 
too  small  and  the  orifice  types  give  results  about  100  per  cent  too  small,  and 
further,  that  none  of  these  meters  give  accurate  comparative  results  for  two  dif- 
ferent oils  or  for  the  same  oil  at  different  temperatures. 

The  only  type  of  viscosimeter  on  the  market  that  can  be  expected  to  give 
accurate  results  on  theoretical  grounds  is  the  Stormer.  This  instrument  at- 
tempts to  measure  the  viscosity  in  terms  of  the  torque  required  to  spin  a disk 
within  the  liquid,  but  the  mechanical  difficulties  met  with  are  such  as  to  debar 
this  type. 

The  authors  have  designed  and  thoroughly  tested  out  a viscosimeter  which 
embodies  all  the  good  points  of  the  Stormer  and  none  of  its  defects.  They 
measure  the  viscosity  in  terms  of  the  torque  which  a cylinder  experiences  when 
suspended  within  a rotating  liquid.  This  method  eliminates  all  error  due  to 
friction.  The  results  given  by  this  meter  agree  with  the  true  curves  for  the  light 
and  medium  oils  to  within  1 per  cent  and  can  safely  be  used  as  a standard. 

The  advantages  of  this  viscosimeter  are  evident.  The  instrument  can  be 
calibrated  to  give  direct  readings  of  the  viscosity;  the  oil  is  not  handled  during 
a complete  test  at  various  temperatures;  the  design  of  the  instrument  is  such 
that  the  temperature  of  the  specimen  follows  closely  the  temperature  of  the  bath, 
so  the  data  for  the  temperature  vs.  viscosity  curve  can  be  taken  while  the  sample 
is  cooling;  the  meter  gives  the  viscosity  of  mixtures,  such  as  paints,  as  well  as 
for  liquids  that  have  been  carefully  filtered;  there  are  no  glass  parts  to  break; 
the  personal  error  is  eliminated  and  the  meter  can  be  made  self  recording. 


1 


THE  MEASUREMENT  OF  VISCOSITY 

AND 

A NEW  FORM  OF  VISCOSIMETER 

By 

H.  C.  Hayes,^  Swarthmore,  Pa.  - 
and 

G.  W.  Lewis, 2 Swarthmore,  Pa. 

Non-members 

In  determining  the  lubricating  properties  of  an  oil,  the  viscosity 
- test  is  considered  of  great  value,  since  by  means  of  this  test  a good 
oil  can  readily  be  distinguished  from  a poor  one.  It  is  therefore 
very  important  that  the  engineer  be  able  to  measure  the  viscosity 
of  an  oil  and  also  the  variation  of  viscosity  with  temperature. 

*2  The  present  paper,  dealing  with  the  measurement  of  viscosity, 
gives  in  part  the  results  of  a somewhat  extended  research  on  the 
lubricating  properties  of  oils.  It  is  to  be  followed  by  a paper  giving 
the  relation  between  the  lubricating  properties  of  oils  and  various 
easily  measurable  physical  properties. 

VISCOSITY 

3 Matter  in  all  states  exhibits  a gradual  yielding  to  tangential 
forces  which  tend  to  change  its  form.  This  property  is  termed 
viscosity  and  may  be  defined  quantitatively  as  the  tangential  force 
per  unit  area  divided  by  the  shear  per  unit  time. 

4 To  gain  a clear  physical  concept  of  this  definition,  consider  a 
plane  surface.  Fig.  1,  of  area>S,  parallel  to  and  at  a distance  d from 
another  large  plane  surface,  and  the  intervening  space  filled  with  a 
liquid  whose  coefficient  of  viscosity  is  rj.  If  a given  force,  F,  acting 
on  this  plane,  is  applied  to  S,  the  surface  will  be  dragged  along  and 

^ Prof,  of  Physics,  Swarthmore  College. 

2 Asst.  Prof,  of  Engrg.,  Swarthmore  College. 

For  presentation  at  the  Spring  Meeting,  New  Orleans,  La.,  April,  1916,  of  The 
American  Society  of  Mechanical  Engineers,  29  West  39th  Street,  New  York. 
All  papers  are  subject  to  revision. 

3 

>01072 


4 


MEASUREMENT  OF  VISCOSITY 


will  finally  attain  a steady  velocity,  which  denote  by  V.  In  accord- 
ance with  the  above  definition,  the  relation  between  these  various 

factors  would  then  be 

r,  = F/S  V/d  or  n = F .d-^  S-V W 

the  value  of  v depending  on  the  units  in  which  these  various  factors 
are  measured.  If  absolute  values  are  desired,  the  factors  on  the 
right  hand  side  of  the  equation  are  to  be  measured  in  C.G.S.  units, 
but  if  relative  values  will  suffice,  as  is  the  case  in  nearly  all  engineering 

work,  they  may  be  measured  in  any  units. 

5 It  must  be  borne  in  mind  that  equation  [1]  is  not  true  w en 
the  velocity,  V,  is  changing,  for  then  only  a part  of  the  force,  F is 
used  to  overcome  viscosity,  a part  being  used  in  giving  acce  era  e 


Fig.  1 Conception  of  Viscosity 

motion.  Under  such  conditions,  another  term  “ust  be  added  to 
this  equation.  The  nature  of  this  term  is  not  difficult  to  see,  for 
!et  equation  [1]  be  written  F=  v-S-V/d.  When  there  is  ac- 
celerated motion,  the  force,  F,  will  be  divided  into  two  Pa^s,  the 
part  used  to  overcome  viscosity  and  that  used  to  give  acce 
motion  Call  these  parts  /i  and  respectively,  then  at  any  instant 
Z T+  f.  where  /=  , • S • F/d  and  /.  = M • dV/dt,  where  M is 
the  mass  that  is  being  accelerated  and  dV/dt  is  the  average  change 
of  velocity  per  second  of  this  mass.  The  complete  instantaneous 
equation  thus  becomes 

F = V SV/d  + M • dV/dt 

and  the  viscosity  cannot  be  found  from  this  equation  unless  the  last 
term  can  be  evaluated,  which  is  usually  difficult  and  often  impossible. 

development  of  a working  formula 
6 In  most  physical  measurements,  comparative  values  are  more 
easily  obtained  than  absolute  values.  As  a result  measurements  aie 
rnTde  Tterms  of  some  standard,  the  absolute  value  of  which  h^ 
been  determined  by  a more  or  less  laborious  proce®.  In  K 

measurements  of  viscosity,  the  standard  usually  chosen  is  water 
a temperature  of  20  deg.  cent. 


H.  C.  HAYES  AND  G.  W.  LEWIS 


5 


7 Girard  and  Poiseuille,  by  studying  the  flow  of  liquids  through 
capillary  tubes,  were  the  first  to  measure  the  absolute  value  of 
viscosity  vdth  anything  like  accuracy.  On  the  basis  of  his  excellent 
experimental  work  on  the  viscosity  of  water,  Poiseuille  deduced  the 
formula 

V = H/L 

where  V = volume  of  liquid  transpired 
L = length  of  capillary 
D = diameter  of  capillary 
H = pressure 

K = constant  for  each  liquid  at  a given  temperature. 

Later,  this  empirical  formula  and  its  corrections  were  proved  by 
several  investigators.’^ 

8 By  assuming  there  is  no  slip  at  the  surface  of  the  capillary, 
that  the  liquid  flows  steadily  without  eddies  or  turbulent  motion, 
and  that  there  is  no  kinetic  energy  of  efflux,  then  the  trans- 
piration formula  for  a liquid  flowing  under  its  own  head  becomes 

‘ ^7  = I Qigr^/lv)  pi 

where  ri  = coefficient  of  viscosity  (often  contracted  to  viscosity) 
h = liquid  head 
g = acceleration  of  gravity 
r = radius  of  capillary 
I = length  of  capillary 
V = volume  of  flow 
t = time  of  flow 
p = density  of  liquid. 

Experiment  shows  that  the  first  assumption  is  true  if  the  liquid  is 
one  that  wets  the  surface  of  the  capillary.  The  work  of  Reynolds 
shows  the  second  assumption  is  true  if  the  velocity  of  the  liquid 
through  the  capillary  is  kept  less  than  700  • ?7/p  • r cm.  per  sec. 
The  third  assumption,  of  course,  can  never  be  true.  The  liquid 

^ Stokes,  Trans.  Camb.  Phil.  Soc.,  1849,  vol.  8,  p.  287;  Wiedmann,  Pog- 
gendorf^s  Annalen,  vol.  99,  p.  177;  Hagenback,  Pogg.  Ann.,  vol.  109,  p.  385; 
Stefan,  Wien.  Bar.,  vol.  46,  p.  495;  Couette,  Ann.  Chim.  Phys.,  vol.  21,  p.  433; 
Neumann,  Vortrage  iiber  Hydrodynamik;  Wilberforce,  Phil.  Mag.,  vol.  31,  p.  407; 
Jacobson,  Arch.  f.  Anat.  u.  Physiol.  1860,  p.  80;  Knibbs,  J.  Roy.  Soc.  N.S.W., 
vol.  29,  p.  77;  Boussinesq,  Compt.  Rend.,  vol.  110,  p.  1160;  Brillouin,  La  Vis- 
cosity (Gauthier  Villars,  1907). 


6 


MEASUREMENT  OF  VISCOSITY 


must  have  kinetic  energy  when  it  leaves  the  capillary-.  In  accord- 
ance with  equation  [2],  a correction  term  must  be  added  which,  ac- 
cording to  Couette,  Finkener,  and  Wilberforce,  should  be  -vp/Sirlt, 
The  complete  expression  for  the  viscosity  is  therefore  of  the  form 

n =p  (A.t-B/t) 

where  A and  B are  constants  for  any  piece  of  apparatus,  p and  t are 
the  density  and  time  of  flow,  respectively. 

9  After  a thorough  examination  of  the  recorded  data  on  the 
viscosity  of  water,  Knibbs  concluded  that  the  correct  formula  should 
be 

^ = Trhgr'^pt/Slv  — lA2vp/STrlt 

It  is  to  be  noted  that  the  correction  term  is  larger  than  that  given  by 
Couette.  Moreover,  this  correction  term  varies  with  the  time  of 
flow  approaching  zero  when  the  velocity  of  flow  is  very  slow,  in  which 
case  t becomes  very  gi'eat.  The  value  of  the  term  increases  with 
the  temperature  of  the  liquid  since  the  time  of  flow  decreases,  and  so 
the  percentage  of  error  in  a viscosity  vs.  temperature  curve  due  to 
neglecting  this  correction  factor  will  increase  abnormally  toward  the 
higher  temperatures.  This  is  due  to  two  causes,  the  correction  to 
be  applied  increases  with  the  temperature  and  the  value  of  the 
quantity  to  be  corrected  decreases  rapidly  with  the  temperature. 
Attention  will  be  called  to  this  fact  when  some  of  the  various  com- 
parative methods  are  discussed.  It  is  further  to  be  noted  that  this 
correction  term  varies  inversely  as  the  length  of  the  capillary.  A 
short  capillary  requires  a large  correction  term. 

10  This  formula,  as  corrected  by  Knibbs  has  been  submitted 
to  careful  experimental  test  by  Hosking,  and  by  Bingham  and 
White.  These  investigators  have  determined  the  constants  of  the 
formula  experimentally  and  have  obtained  fair  agreement  with 
theory.  The  capillary  tube  method,  as  employed  by  these  experi- 
menters, though  complicated  and  laborious,  can  be  depended  upon 
for  giving  absolute  values  of  the  viscosity,  and  the  accuracy  of  any 
viscosimeter  can  be  determined  by  a comparison  with  the  results 
obtained  by  this  method. 

CLASSIFICATION  OF  VISCOSIMETERS 

11  Class  1.  Short  Capillary.  In  meters  of  this  type,  the  liquid 
to  be  tested  is  forced  either  by  gravity  or  by  pressure  through  tlie 
capillary  and  the  viscosity  is  determined  in  terms  of  the  time  re- 


H.  C.  HAYES  AND  G.  W.  LEWIS 


7 


quired  for  a given  volume  to  pass  through  the  meter,  as  compared 
with  the  time  required  for  a standard  liquid  to  discharge  the  same 
volume. 

12  A cross  section  of  a meter  of  this  type  is  shown  in  Fig.  2. 
The  essential  parts  of  the  instrument  are  a cylindrical  bowl,  A,  in 
which  the  oil  is  placed  and  a short  capillary  tube  B,  through  which 
it  is  discharged.  The  instrument  must  have  temperature  controlling 
and  measuring  devices,  means  for  starting  and  stopping  the  flow  and 
volume  and  time  measuring  apparatus. 

13  To  this  class  belong  the  Saybolt  meter,  adopted  as  a standard 
by  the  Standard  Oil  Co.;  the  Engler  meter,  adopted  as  a standard 
by  the  U.  S.  Government  and  Germany;  the  Redwood  meter. 


Fig.  2 Short  Capillary  Type  Viscosimeter 

adopted  as  a standard  in  England ; the  Scott  meter ; and  the  pipette, 
adopted  as  a standard  by  the  Pennsylvania  Railroad  and  much  used 
by  chemists.  The  majority  of  the  viscosimeters  on  the  market  are 
of  the  short  capillary  type. 

14  Class  2.  Orifice.  This  type  employs  an  orifice  in  place  of 
the  short  capillary  of  the  previous  type.  Fig.  3 is  a section  of  such 
a meter,  in  the  cylindrical  bowl.  A,  of  which  the  oil  to  be  tested  is 
kept  at  constant  head  above  the  orifice,  B.  The  Carpenter  meter 
belongs  to  this  class. 

15  Class  3.  Dropping  a solid  body  through  a luhe  filled  with  the 
liquid,  the  solid  body  being  usually  a sphere  or  a plunger.  Meters 
emplojdng  this  principle  determine  the  viscosity  in  terms  of  the 


8 


MEASUREMENT  OF  VISCOSITY 


time  required  for  the  body  to  drop  a certain  distance  through  the 
liquid,  as  compared  with  the  time  required  for  the  same  body  to  drop 
through  a standard  liquid.  To  this  class  of  meters  belong  the 
Perkins  meter  which  employs  a plunger  and  vertical  tube,  and  the 


Fig.  3 Orifice  Type  Viscosimeter 

Flowers  meter  ^which  employs  a small  steel  sphere  and  a slanting- 
tube.  |i 

16  Class  4.  Oscillating  Disk  or  Cylinder.  These  meters  de- 
termine the  viscosity  in  terms  of  the  damping  which  the  oscillating 
disk  or  cylinder  experiences  when  placed  in  the  liquid  as  compared 
with  the  damping  when  placed  in  the  standard  liquid.  The  Doo- 
little meter  is  an  example  of  this  class. 


H.  C.  HAYES  AND  G.  W.  LEWIS 


9 


17  Class  5.  Rotating  Disk  or  Cylinder.  This  type  determines 
the  viscosity  in  terms  of  the  speed  of  rotation  of  the  disk  or  cylinder 
in  the  liquid  under  test  as  compared  with  the  speed  of  rotation  in 
the  standard,  the  driving  torque  remaining  constant.  The  Stormer 
meter  is  an  example  of  this  class. 

DISCUSSION  OF  THE  VAKIOUS  TYPES 

18  The  value  of  each  of  the  above  types,  so  far  as  accuracy  is 
concerned,  can  be  estimated  by  noting  whether  they  operate  in  ac- 
cordance Avith  equation  [1]  or  [2],  but  before  speaking  of  the  various 
types  it  should  be  noted  that  only  equation  [1]  will  give  accurate 
comparative  results. 

19  Write  this  equation  in  the  forms 

yfx  ~ F X * dx/ F>x  • T X 

where  the  subscript  x refers  to  the  substance  and  conditions  met 
with  in  connection  with  the  liquid  to  be  tested,  and 

Vs=  Fs-dJS,.\\ 

where  the  subscript  s refers  in  a similar  manner  to  the  standard 
liquid.  Solving  these  two  equations  for  y gives 

rix  = Vs  • S,.V,-Fx-  dx/F, . d, . .S, . TT 

an  expression  which  simplifies  to 

= r;,  (Fx/F,) 

if  the  same  apparatus  is  used  in  both  cases,  whereas  if  we  apply  the 
same  operation  to  equation  [2]  we  get 

V.  = Vs  [Fx  - . dVx/dtx)/{F,  - M, . dVJdQ]  VJVx 

20  This  expression  cannot  be  simplified,  for  the  expression 
within  the  brackets  can  never  be  made  equal  to  unity.  Moreover 
this  expression  is  not  constant,  but  varies  with  every  liquid  which 
is  compared  with  the  standard  and  with  every  change  of  temperature. 
It  is  therefore  impossible  to  assign  an  accurate  correction  factor  to 
an  instrument  which  seeks  comparative  results  if  the  instrument 
operates  in  accordance  with  equation  [2],  or,  in  other  words,  if  there 
is  any  accelerated  motion  of  the  liquid  during  the  testing  operation. 

21  In  practice,  the  time,  t,  required  for  a definite  volume  of 
liquid  to  pass  through  the  meter  is  measured  instead  of  the  velocity, 
V,  and,  if  the  force  driving  the  liquid  is  gravity,  the  force  F is  easily 


10 


MEASUREMENT  OF  VISCOSITY 


evaluated  as  p • A,  where  p is  the  density  and./i  the  average  head. 
Equations  [1]  and  [2],  in  practice,  thus  become 

Vx=  Vs-ix-t,.  h/t,  • p,-h  or  - = [la] 

Vx  = Vs  - tx/t,[px  • Ti  - (M^ . dVx/dQ/(p,  .h  - M,-  dVJdQ]. [2a] 

THE  ACCELERATION  ERROR 

22  It  is  obvious  that  equation  [2a]  applies  to  all  meters  coming 
under  Classes  1 and  2 since  the  liquid  starts  from  rest  in  the  meter 
chamber  and  leaves  with  a certain  velocity  and  must  therefore 
experience  acceleration.  In  all  these  meters  on  the  market  the  ac- 
celeration term  (M  • dV I dt)  is  neglected  since  its  evaluation  is  im- 
possible and  the  formula  then  becomes  identical  with  equation  [la]. 
An  error  which  we  shall  call  the  acceleration  error  is  thereby  intro- 
duced. 

23  The  nature  of  this  error  can  be  predicted  from  an  inspection 
of  equation  [2a].  The  liquid  having  the  smaller  viscosity  will  pass 
through  the  meter  with  the  greater  velocity  and  the  correction  term 
(M  . dV I di)  will  be  larger  in  proportion  for  this  than  for  the  more 
viscous  liquid.  If,  therefore,  water  is  chosen  as  a standard  in  de- 
termining the  viscosity  of  lubricating  oil  or  any  liquid  which  is  more 
viscous  than  itself,  the  value  [(E  — M • dV/dt)/{F  — M • dV /di)] 
will  be  larger  than  the  value  F /F  and  the  value  r?  as  computed  from 
the  approximate  formula  [la]  will  be  too  small.  If,  however,  the 
liquid  under  test  has  a smaller  viscosity  than  the  standard  the 
bracketed  term  will  have  a smaller  value  than  F /F  and  the  result  as 
given  by  the  approximate  formula  will  be  too  large. 

24  In  the  case  of  meters  employing  capillary  flow,  it  is  evident 
that  the  acceleration  term  will  increase  with  the  diameter  of  the 
capillary  and  decrease  with  its  length  and,  as  a result,  we  shall  expect 
all  meters  using  short  capillaries  to  be  subject  to  large  error.  More- 
over, if  we  regard  the  orifice  as  a very  short  capillary,  we  should 
expect  the  error  introduced  in  this  type  of  meter  to  be  still  greater. 
The  experimental  results  presented  later  prove  these  predictions  to 
be  correct. 

SURFACE  TENSION  ERROR 

25  Another  error  introduced  in  all  the  flow  type  viscosim- 
eters, of  both  the  capillary  and  orifice  forms,  is  due  to  difference 
in  the  surface  tension  of  the  standard  liquid  and  the  liquid  under 


H.  C.  HAYES  AND  G.  W,  LEWIS 


11 


test.  This  error  is  prominent  for  those  meters  which  discharge  from 
the  capillary  or  orifice  into  the  air.  As  soon  as  the  stream  leaves  the 
meter  the  film  which  forms  on  the  free  surface  tends  to  contract,  and 
thus  decreases  the  cross  section  of  the  stream  and  retards  the  dis- 
charge. This  contraction  is  greater  for  a liquid  of  high  than  for  one 
of  low  surface  tension.  If  water  is  used  as  the  standard,  since  its 
surface  tension  is  greater  than  for  oils  the  flow  of  water  will  be  re- 
tarded more  than  the  flow  for  oils.  The  time  of  flow,  will  be  in- 
creased in  greater  proportion  than  tx,  thus  giving  the  ratio  tx/ts, 
too  small  and  the  error  will  cause  the  value  to  be  too  small.  For 
oils  and  most  liquids,  the  surface  tension  error  and  the  acceleration 
error  are  additive. 

26  This  surface  tension  effect  is,  of  course,  negligible  for  a stream 
having  high  velocity,  as  the  inertia  of  the  moving  mass  prevents  dis- 
tortion of  the  stream  lines.  For  the  low  velocities  of  efflux  given  by 
flow  type  viscosimeters,  however,  the  effect  is  very  noticeable,  as  can 
be  seen  by  measuring  the  diameter  of  the  efflux  for  two  liquids  of 
different  surface  tension.  When  conditions  are  most  favorable  for 
reducing  the  acceleration,  namely  velocity  of  efflux  very  small,  they 
are  most  favorable  for  introducing  the  surface  tension  error. 

CKITICAL  VELOCITY  ERROR 

27  Another  source  of  error  in  most  capillary  and  orifice  forms  of 
viscosimeters  is  that  the  dimensions  of  the  instrument  are  such  that 
for  the  standard  — water  — the  flow  exceeds  the  critical  velocity 
and  the  resulting  turbulent  flow  makes  the  value  of  t abnormally 
large.  This  introduces  an  error,  which  also  adds  itself  to  the  ac- 
celeration and  surface  tension  errors.  This  fact  was  discovered 
during  the  research  work  about  to  be  recorded  but  has,  in  the  mean- 
time been  noted  and  investigated  by  Upton  who  found  the  error  so 
introduced  by  the  Engler  viscosimeter  to  be  great. 

28  The  three  errors  — acceleration,  surface  tension  and  critical 
velocity  — are  prominent  in  all  the  meters  named  above  as  standards 
and  we  should  expect  the  viscosity  as  given  by  these  meters  to  be 
in  general  much  too  low.  The  experimental  results  will  show  that 
it  is. 

29  Those  meters  based  on  the  principle  of  dropping  a solid 
body  through  a tube  filled  with  the  liquid  to  be  tested  should  be 
more  accurate  than  the  capillary  or  orifice  forms  as  they  are  free 
from  the  surface  tension  error  and  usually  from  the  critical  velocity 


12 


MEASUREMENT  OF  VISCOSITY 


error.  All  are,  however,  subject  to  the  acceleration  error.  All  the 
liquid  displaced  by  the  falling  body  suffers  acceleration.  These 
meters  are  all  of  the  flow  type  and  may  be  regarded  as  of  the  short 
capillary  form,  the  reduced  section  at  the  point  where  the  falling 
body  is  passing  being  the  capillary.  The  liquid  flows  across  this 
section  as  truly  as  it  does  through  the  orifice  or  capillary. 

30  The  relation  between  the  damping  which  an  oscillating  disk 
or  cylinder  experiences  and  the  viscosity  of  the  liquid  in  which  it  is 
immersed  is  complicated,  and  indeed  the  true  relation  is  not  known. 
Meters  based  on  this  principle,  such  as  the  Doolittle  meter,  do  not 
give  accurate  results.  They  are  nearly  free  from  the  surface  tension 
and  critical  velocitv  errors,  however,  and  though  somewhat  slow  and 
difficult  to  operate,  they  give  better  results  than  the  majority  of  flow 
types. 

31  The  constant  speed  of  rotation  which  a disk  or  cylinder 
immersed  in  a liquid  will  attain  under  the  action  of  a constant  torque 
is  a true  measure  of  the  viscosity  of  the  liquid.  The  Stormer  viscos- 
imeter attempts  to  operate  in  accordance  with  this  principle,  but  the 
friction  of  the  moving  parts  is  necessarily  such  that  a constant 
torque  cannot  be  obtained.  With  proper  refinement,  this  meter 
could  be  made  to  give  good  results.  The  fact  that  a meter  based  on 
this  principle  can  theoretically  give  accurate  results  has  led  to  the 
development  of  a new  viscosimeter  now  to  be  described. 

THE  NEW  VISCOSIMETER 

32  This  viscosimeter  operates  in  accordance  with  the  principle 
that  a solid  body  having  a surface  of  revolution  experiences,  when 
suspended  in  a rotating  liquid,  a torque  which  is  proportional  to  the 
viscosity  of  the  liquid.  The  instrument  is  shown  diagramatically 
in  Fig.  4.  The  specimen,  S,  is  contained  within  a cylindrical  chamber 
Tvhich  is  caused  to  rotate  uniformly  by  a motor,  M,  through  a worm 
drive,  R.  A cylinder,  C,  is  suspended  within  the  specimen  by  a 
thin  steel  wire,  W,  so  that  the  axis  of  the  rotating  liquid  coincides 
with  the  axis  of  the  cylinder.  The  specimen  chamber  is  provided 
with- a cap,  V,  so  shaped  that  the  excess  liquid  can  overflow  when  the 
cap  is  seated  and  thus  give  constant  conditions  within  the  chamber. 
The  specimen  chamber  is  surrounded  by  an  oil  jacket,  J,  in  which 
a thermometer,  T,  is  suspended.  The  jacket  oil  may  be  brought  to 
any  desired  temperature  by  means  of  a heating  coil,  or  a side  coil 
not  shown  in  the  diagram.  The  cover,  P,  of  the  jacket  chamber 


H.  C.  HAYES  AND  G.  W.  LEWIS 


13 


is  provided  with  a scale  which  is  marked  in  degrees  or  may  be  cali- 
brated to  read  off  directly,  through  the  deflection  of  the  pointer,  P, 
the  viscosity  in  terms  of  a standard  liquid.  The  specimen  chamber 
and  the  suspended  cylinder  are  both  made  of  copper  to  insure  con- 
stant temperature  throughout  the  specimen  and  the  outside  of  the 
specimen  chamber  is  provided  with  blades  which  keep  the  jacket 


oil  thoroughly  mixed  as  the  chamber  revolves  and  thereby  exposes 
the  latter  to  a uniform  temperature.  This  is  an  important  factor 
toward  insuring  constant  temperature  throughout  the  specimen. 

33  The  experimental  work  has  shown  that  the  temperature  of 
the  specimen  is  uniform  to  within  a small  fraction  of  a degree.  More- 
over, the  temperature  of  the  specimen  follows  the  temperature  of 
the  jacket  oil  so  closely  that  the  temperature-viscosity  curve  can  be 
taken  while  the  temperature  is  slowly  raised  or  lowered.  This 


14 


MEASUREMENT  OF  VISCOSITY 


proves  to  be  a great  saving  of  time.  It  also  saves  labor,  for  one 
does  not  need  to  stand  by  the  instrument  continually.  The  de- 
flection of  the  pointer  is  at  any  instant  a measure  of  the  viscosity,  so 
all  that  is  required  is  to  take  simultaneous  readings  of  temperature 
and  deflection  at  intervals  during  the  heating  or  cooling  process. 

EXPERIMENTAL  RESULTS 

34  To  test  the  accuracy  of  this  viscosimeter,  the  temperature- 
viscosity  curve  was  found  for  a light  and  a medium  gas  engine  oil 
by  the  capillary  tube  method,  the  apparatus  for  which  is  shown  in 


Fig.  5.  The  oil  was  drawn  from  vessel  A to  vessel  B,  and  vice  versa, 
by  connecting  each  in  turn  with  the  partial  vacuum  chamber,  C. 
These  vessels  were  submerged  in  a thermostat  which  could  be  main- 
tained at  any  desired  temperature.  The  results,  in  terms  of  the 
viscosity  of  water  at  20  deg.  cent.,  are  given  by  the  points  enclosed 
in  circles  for  curves  1 and  la.  Figs.  6 and  7,  the  latter  referring 
to  the  lighter  oil.  The  viscosity  of  these  same  oils  as  given  by  the 
new  meter  is  represented  on  curves  1 and  la  by  the  points  enclosed 
in  squares.  The  agreement  between  the  two  methods  is  almost 
perfect. 

35  The  viscosity  of  these  oils  as  given  by  a meter  of  the  short 
capillary  type.  Fig.  2,  is  given  in  curves  2 and  2a.  Curves  3 and  3a 
give  the  viscosity  of  these  oils  as  obtained  with  a meter  of  the  orifice 
form.  Fig.  3.  As  predicted,  the  results  given  by  the  short  capillary 


V'iCO&ifi)  Viscosi+y 


n.  C.  HAYES  AND  G.  W.  LEWIS 


15 


Temperature,  Dey.  Fa  hr. 

Fig.  6 Viscosity  Curves  for  Medium  Gas  Engine  Oil 


Fig.  7 Viscosity  Curves  for  Light  Gas  Engine  Oil 


16 


MEASUREMENT  OF  VISCOSITY 


type  are  much  too  low  (on  the  oils  tested  about  100  per  cent  too  low) 
and  the  results  given  by  the  orifice  type  are  still  lower. 

CONCLUSIONS 

36  The  errors  inherent  in  all  flow  types  of  viscosimeters  have 
been  predicted  and  the  predictions  verified  by  experiment.  The 
magnitude  of  the  errors  are  such  that  these  meters  cannot  be  de- 
pended on  for  giving  even  approximate  results.  The  various  meters 
of  this  type  on  the  market  do  not  give  results  which  are  in  agree- 
ment, and  no  one  of  these  meters  can  justly  be  claimed  as  a standard. 

37  The  new  viscosimeter  of  the  non-flow  type  described  has  the 
following  advantages: 

1 It  gives  values  for  the  viscosity  which  are  in  agreement 

with  those  given  by  the  standard  capillary  tube  method. 

2 During  a series  of  tests  at  various  temperatures,  the  oil 

is  not  handled. 

3 The  sensitiveness  of  the  instrument  can  be  made  any- 

thing desired  by  changing  the  speed  of  rotation  of  the 
specimen  or  by  using  suspension  wires  of  various  diam- 
eters. 

4 The  density  or  change  in  density  is  not  a factor  in  com- 

puting the  results,  in  fact  the  instrument  may  be  gradu- 
ated to  read  off  the  viscosity  directly. 

5 The  viscosity  of  liquids  which  contain  particles  in  sus- 

pension can  be  measured,  and  the  operation  of  the  meter 
is  independent  of  the  color  of  the  specimen. 

6 The  temperature-viscosity  curve  can  be  taken  with  a fair 

degree  of  accuracy  while  the  temperature  is  rising  or 
falling,  as  the  temperature  of  the  specimen  follows  the 
temperature  of  the  jacket  so  closely. 

7 The  personal  error  which  arises  in  determining  time  in- 

tervals with  a stop  watch  is  removed. 

8 The  instrument  is  simple,  rigid  and  self-contained.  It 

has  no  separate  parts  to  get  lost  or  glass  parts  to  get 
broken. 


UNIVERSITY  OF  ILLINOIS-URBANA 


